Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
consider the given function: f(x)= √x-4
To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.
The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.

Answer 1

Answer:

• Blank 1: $x$

• Blank 2: $y$

• Blank 3: 4

• Blank 4: 4

Explanation:

The function under consideration is:

   $f(x)=\sqrt{x-4}$

And the work is to state the steps to determine the inverse of the given function and to present the resulting inverse function of f(x).

1. First step:

Change    $f(x)$    to    $y$  

This is to work algebraically with a variable instead with the name of the function.

Result:     $y=\sqrt{x-4}$

2. Second step:

Switch $\underline{\text{ }x\text{ }}$ and $y$ , and solve for $\underline{\text{ }y\text{ }}$.

Result:

$x=\sqrt{y-4}\\ \\ x^2=y-4\\ \\ x^2+4=y\\ \\ y=x^2+4$

3. Third step:

Now you can change    $y$    to    $f^{-1}(x)$

Result:

$f^{-1}(x)=x^2+4$

4. Fourth step

State the domain of the function.

Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.

Hence, the final blank is 4.

Answer 2

Answer:

switch: x, Solve for: y, x^2+: 16, x is greater than 0

Step-by-step explanation: